Methods of making an unsupported article of semiconducting material by controlled undercooling

ABSTRACT

The invention relates to methods of making articles of semiconducting material and semiconducting material articles formed thereby, such as semiconducting material that may be useful in making photovoltaic cells.

FIELD

The invention relates generally to methods of making articles ofunsupported semiconducting materials by controlled undercooling.

BACKGROUND

Semiconducting materials find uses in many applications. For example,semiconducting materials can be used in electronic devices as processorsformed on semiconductor wafers. As a further example, semiconductingmaterials can be used to convert solar radiation into electrical energythrough the photovoltaic effect.

The semiconducting properties of a semiconducting material may depend onthe crystal structure of the material. Notably, faults within thecrystal structure of a semiconducting material may diminish thematerial's semiconducting properties.

The grain size and shape distribution often play an important part inthe performance of semiconducting devices where a larger and moreuniform grain size is often desirable. For example, the electricalconductivity and efficiency of photovoltaic cells may be improved byincreasing grain size and the uniformity of grains.

For silicon-based solar photovoltaic cells, the silicon can, forexample, be formed as an unsupported sheet, or can be supported byforming the silicon on a substrate. Conventional methods for makingunsupported and supported articles of semiconducting materials, such assilicon sheets, have several shortcomings. Methods of makingunsupported, i.e., without an integral substrate, thin semiconductingmaterial sheets may be slow or wasteful of the semiconducting materialfeedstock.

Methods by which unsupported single crystalline semiconducting materialsare made include, for example, the Czochralski process, which may leadto significant kerf loss when the semiconducting material is sliced orcut into a thin sheets or wafers. Methods by which unsupportedmulticrystalline semiconducting materials are made include, for example,electromagnetic casting and ribbon growth techniques, which may be slow,producing about 1-2 cm/min for polycrystalline silicon ribbon growthtechnologies.

Other useful methods for producing unsupported multicrystallinesemiconducting material are disclosed in U.S. Provisional PatentApplication No. 61/067,679, filed Feb. 29, 2008, titled “METHOD OFMAKING AN UNSUPPORTED ARTICLE OF A PURE OR DOPED SEMICONDUCTING ELEMENTOR ALLOY,” the disclosure of which is hereby incorporated by reference.

Supported semiconducting material sheets may be made less expensively,but the thin semiconducting material sheet is limited to the substrateon which it is made, and the substrate has to meet various process andapplication requirements, which may be conflicting.

Thus, there is a long-felt need in the industry for a method to makeunsupported articles of semiconducting materials, which method mayimprove crystal grain structure of the article of semiconductingmaterial, reduce material waste, and/or increase the rate of production.

SUMMARY

In accordance with various exemplary embodiments of the invention areprovided methods of making an unsupported article of semiconductingmaterial comprising providing a mold at a temperature T₀, providing amolten semiconducting material at a bulk temperature T_(Melt), whereinT_(Melt)≧T₀, immersing the mold in the molten semiconducting material atleast once for a first period of time sufficient to form a solid layerof the semiconducting material over an external surface of the mold andfor the formed solid layer of semiconducting material to completelyremelt, withdrawing the mold from the molten semiconducting material,holding the mold above the molten semiconducting material for a periodof time sufficient to undercool the mold a predetermined amount,immersing the mold in the molten semiconducting material for a secondperiod of time sufficient to form a solid layer of the semiconductingmaterial over the external surface of the mold, withdrawing the moldwith the solid layer of semiconducting material over the externalsurface of the mold, and separating the solid layer of semiconductingmaterial from the mold to form the unsupported article of thesemiconducting material.

Other exemplary embodiments relate to methods of making an article ofsemiconducting material comprising providing a mold at a temperature T₀,wherein the mold comprises a surface comprising a primary material andat least one secondary material at discrete locations, the secondarymaterial having a contact angle with a molten semiconducting materialthat is less than the contact angle between the primary material and themolten semiconducting material, providing the molten semiconductingmaterial at a bulk temperature T_(Melt), wherein T_(Melt)≧T₀, immersingthe mold in the molten semiconducting material at least once for a firstperiod of time sufficient to form a solid layer of the semiconductingmaterial over the surface of the mold and for the formed solid layer ofsemiconducting material to completely remelt, withdrawing the mold fromthe molten semiconducting material, holding the mold above the moltensemiconducting material for a period of time sufficient to undercool themold a predetermined amount, immersing the mold in the moltensemiconducting material for a second period of time sufficient to form asolid layer of the semiconducting material over the surface of the mold,withdrawing the mold with the solid layer of semiconducting materialover the external surface of the mold, and separating the solid layer ofsemiconducting material from the mold to form the unsupported article ofthe semiconducting material.

Exemplary embodiments of the invention also relate to articles ofsemiconducting material formed by a method comprising providing a moldat a temperature T₀, providing a molten semiconducting material at abulk temperature T_(Melt), wherein T_(Melt)≧T₀, immersing the mold inthe molten semiconducting material for a first period of time sufficientto form a solid layer of the semiconducting material over an externalsurface of the mold and for the formed solid layer of semiconductingmaterial to completely remelt, withdrawing the mold from the moltensemiconducting material, holding the mold above the moltensemiconducting material for a period of time sufficient to undercool themold a predetermined amount, immersing the mold in the moltensemiconducting material for a second period of time sufficient to form asolid layer of the semiconducting material over the external surface ofthe mold, withdrawing the mold with the solid layer of semiconductingmaterial over the external surface of the mold, and separating the solidlayer of semiconducting material from the mold to form the unsupportedarticle of the semiconducting material.

The methods according to the present invention may, in at least someembodiments, improve the crystal grain structure of semiconductingmaterials, reduce material waste, and/or increase the rate of productionof articles of the semiconducting material.

As used herein, the term “semiconducting material” includes materialsthat exhibit semiconducting properties, such as, for example, silicon,germanium, tin, gallium arsenide, as well as alloys, compounds, andmixtures thereof. In various embodiments, the semiconducting materialmay be pure (such as, for example, intrinsic or i-type silicon) or doped(such as, for example, silicon containing a n-type or p-type dopant,such as phosphorous or boron, respectively).

As used herein, the phrase “article of semiconducting material” includesany shape or form of semiconducting material made using the methods ofthe present invention. Examples of such articles include articles thatare smooth or textured; articles that are flat, curved, bent, or angled;and articles that are symmetric or asymmetric. Articles ofsemiconducting materials may comprise forms such as, for example, sheetsor tubes.

As used herein, the term “unsupported” means that an article ofsemiconducting material is not integral with a mold. The unsupportedarticle may be loosely connected to the mold while it is being formed,but the article of semiconducting material is separated from the moldafter it is formed over the mold. The unsupported article may, however,be subsequently applied on a substrate for various applications, such asphotovoltaic applications.

As used herein, the term “mold” means a physical structure that caninfluence the final shape of the article of semiconducting material.Molten or solidified semiconducting material need not actuallyphysically contact a surface of the mold in the methods describedherein, although contact may occur between a surface of the mold and themolten or solidified semiconducting material.

As used herein, the term “external surface of the mold” means a surfaceof the mold that may be exposed to a molten semiconducting material uponimmersion. For example, the interior surface of a tube-shaped mold maybe an external surface if the internal surface can contact a moltensemiconducting material when the mold is immersed.

As used herein, the phrase “form a solid layer of semiconductingmaterial over an external surface of the mold” and variations thereofmean that semiconducting material from the molten semiconductingmaterial solidifies (also referred to herein as freezing orcrystallizing) on or near an external surface of the mold. Forming asolid layer of semiconducting material over an external surface of themold may, in some embodiments, include solidifying semiconductingmaterial on a layer of particles that coat the external surface of themold. In various embodiments, due to the temperature difference betweenthe mold and the molten semiconducting material, the semiconductingmaterial may solidify before it physically contacts the surface of themold. When the semiconducting material solidifies before it physicallycontacts the mold, the solidified semiconducting material may, in someembodiments, subsequently come into physical contact with the mold orwith particles coating the mold. The semiconducting material may, insome embodiments, also solidify after physically contacting the externalsurface of the mold, or particles coating the surface of the mold, ifpresent.

As used herein, the phrase “templated mold” means a mold having asurface comprising a primary material and discrete locations of at leastone secondary material exposed to the molten semiconducting material.The primary material and at least one secondary material may havedifferent contact angles with the molten semiconducting material andthus, different nucleation properties with the molten semiconductingmaterial. For example, a templated mold may comprise a primary materialhaving a high contact angle with the molten semiconducting material andat least one secondary material having a lower contact angle with themolten semiconducting material. The templated mold according to theinvention may have any arrangement of at least one secondary material onthe surface of the mold, such as, for example, various patterns of dotscomprising the at least one secondary material on a surface of theprimary material.

As used herein, the phrase “increased rate of production” and variationsthereof includes any increase in the rate of semiconducting materialarticle production with respect to conventional methods for producingsemiconducting material, such as ribbon growth methods. For example, anincreased rate of production may be any rate greater than about 1-2cm/min.

As used herein, the phrase “reduced material waste” and variationsthereof means any reduction in the amount of semiconducting materiallost through conventional methods using slicing or cutting followingproduction of the article of semiconducting material.

As used herein, the term “crystalline” means any material comprising acrystal structure, including, for example, single crystalline andmulticrystalline materials.

As used herein, the term “multicrystalline” includes any materialcomprised of a plurality of crystal grains. For example,multicrystalline materials may include polycrystalline,microcrystalline, and nanocrystalline materials.

As used herein, the term “crystal grain structure” includes grain size,grain shape, uniformity of grain size, uniformity of grain shape, and/oruniformity of grain direction. An improvement in the crystal grainstructure may include, for example, an increase in grain size oruniformity of grain size and/or shape, and/or may reduce the amount ofpost-processing the article of semiconducting material may undergo ascompared to conventional methods for producing semiconducting material.

As used herein, the term “undercooling” refers to a process in which atemperature difference is generated between the molten semiconductingmaterial and the mold that may cause solidification (also referred toherein as freezing) of the molten semiconducting material, and theamount of undercooling may be measured in degrees Kelvin (K) or Celsius(° C.). The term “controlled undercooling” means the amount ofundercooling is a set or predetermined amount that may be controlled bythe methods of the invention.

As used herein, the term “nucleation rate” means the rate at which newcrystal seeds form and may be measured in number of seeds per unit area.

As used herein, the term “equiaxed growth” means the formation of manysmall grains with random orientations. Equiaxed growth may occur, forexample, at the beginning of the crystallization process, such as when amold is initially immersed in molten semiconducting material. Equiaxedgrowth may occur in a generally planar direction with respect to thesurface of a mold.

As used herein, the term “columnar growth” means the growth of crystalsin a direction normal to the surface of a mold such that a crystaldimension parallel to the growth direction is greater than a crystaldimension perpendicular to the growth direction.

As used herein, the terms, “temperature of the molten semiconductingmaterial,” “bulk temperature of the molten semiconducting material,” andvariations thereof mean the average temperature of the moltensemiconducting material contained within a suitable vessel. Localizedtemperatures within the molten semiconducting material may vary at anypoint in time, such as, for example, areas of the molten semiconductingmaterial proximate to the mold when the mold is immersed, or moltensemiconducting material exposed to atmospheric conditions at the topsurface of the vessel. In various embodiments, the average temperatureof the molten semiconducting material is substantially uniform despiteany localized temperature variation.

As described herein, the invention relates to methods of making articlesof semiconducting material and semiconducting material articles formedthereby. In the following description, certain aspects and embodimentswill become evident. It should be understood that the invention, in itsbroadest sense, could be practiced without having one or more featuresof these aspects and embodiments. It should be understood that theseaspects and embodiments are merely exemplary and explanatory, and arenot restrictive of the invention as claimed.

BRIEF DESCRIPTION OF DRAWINGS

The following figures, which are described below and which areincorporated in and constitute a part of the specification, illustrateexemplary embodiments of the invention and are not to be consideredlimiting of the scope of the invention, for the invention may admit toother equally effective embodiments. The figures are not necessarily toscale, and certain features and certain views of the figures may beshown exaggerated in scale or in schematic in the interest of clarityand conciseness.

FIG. 1 is a schematic illustration of an exemplary method of making anunsupported article of semiconducting material according to anembodiment of the invention;

FIG. 2 is a representative calculated plot of the thickness of a siliconarticle formed as a function of the immersion time in molten silicon;

FIG. 3 is a graph illustrating the calculated and measured temperatureof a mold as a function of time after removing the mold from a bath ofmolten semiconducting material;

FIG. 4 is a graph illustrating the time needed to cool a mold whileholding it above the melt after removing it from the melt as a functionof the desired undercooling of the mold at different levels of surfacethickness;

FIG. 5 is a graph illustrating the calculated thickness of a siliconarticle as a function of the immersion time at different levels ofundercooling and different levels of substrate thickness;

FIG. 6 is a schematic representation of a templated mold;

FIG. 7 is a graph illustrating calculated nucleation rates of siliconhomogeneous nucleation, heterogeneous nucleation on fused silica, andheterogeneous nucleation on silicon carbide as a function ofundercooling; and

FIG. 8 is a schematic representation of an exemplary immersion angle ofa mold as it is immersed in molten semiconducting material.

DETAILED DESCRIPTION

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory only,and are not restrictive of the invention, as claimed. Other embodimentsof the invention will be apparent to those skilled in the art fromconsideration of the specification and practice of the inventiondisclosed herein. It is intended that the specification be considered asexemplary only.

FIG. 1 illustrates an exemplary method of making an unsupported articleof a semiconducting material according to at least one embodiment of theinvention. The exemplary method is an exocasting process, which caststhe article over an exterior surface of a mold, rather than within aninternal mold cavity. A mold 100 is provided having an external surface102 with a desired size (surface area), shape, and surfacetexture/pattern. The surface area, shape, and surface texture/pattern ofthe external surface 102 of the mold 100 may determine the size, shape,and surface texture/pattern of the cast article. One of ordinary skillin the art would recognize that the size, shape, and surfacetexture/pattern of the external surface 102 of the mold 100 can beselected based on, for example, the desired properties and features ofthe cast article.

Molten semiconducting material 104 such as, for example, silicon, may beprovided by melting silicon in a vessel 106, such as a crucible, whichmay optionally be non-reactive with the silicon. In at least oneembodiment, molten semiconducting material 104 may have low contaminantlevels. For example, molten semiconducting material 104 may compriseless than about 1 ppm of iron, manganese, and chromium, and less thanabout 1 ppb of vanadium, titanium, and zirconium. Molten semiconductingmaterial 104 may also comprise less than about 10¹⁵ atoms/cm³ ofnitrogen and/or 10¹⁷ atoms/cm³ of carbon. In at least one embodiment,the source of the semiconducting material may be photovoltaic-gradesilicon or purer silicon.

In one exemplary embodiment, the molten semiconducting material 104 maybe brought to a bulk temperature, T_(Melt), in a low oxygen or reducingatmosphere using any suitable heating device or method. The bulktemperature of the molten semiconducting material, T_(Melt), may also bemaintained at that temperature by any suitable heating device or method.Suitable heating devices and methods include heating elements, such asresistive or inductive heating elements, and a flame heat source. Oneskilled in the art would recognize that the choice of a heat source maybe made based on several factors such as, for example, the capacity ofthe vessel containing the molten semiconducting material, thesize/thickness of the vessel, and/or the atmosphere surrounding thevessel.

In at least one embodiment, the bulk temperature of moltensemiconducting material, T_(Melt), may be the melting temperature of thesemiconducting material, or may be a higher temperature. In oneexemplary embodiment where the semiconducting material comprisessilicon, the bulk temperature of the molten silicon may range from about1414° C. to about 1550° C., such as, for example, from about 1450° C. toabout 1490° C.

In at least one embodiment of the invention, mold 100 at a startingtemperature, T₀ (i.e., T_(Mold) at time, t=0), may be provided in a lowoxygen or reducing atmosphere. The starting temperature of mold, T₀, mayin at least some embodiments be chosen so that T₀≦T_(Melt). According toat least one embodiment of the invention, mold 100 is not pre-heatedprior to immersing mold 100 in molten semiconducting material 104. In atleast one embodiment of the invention, the temperature of mold 100 isaltered only by the molten semiconducting material 104 and by theatmosphere outside of vessel 106, i.e., the temperature of mold 100 isnot directly regulated by any heating or cooling devices.

According to at least one embodiment, the mold 100 may be immersed inthe molten semiconducting material at least two times. According to atleast one embodiment, the mold 100 is immersed at least once for a timesufficient such that mold 100 may reduce the temperature of the moltenmaterial in close proximity to the external surface of mold 100 to thefreezing point of the semiconducting material 104 and to removesufficient heat from the molten semiconducting material 104 to freeze atleast a portion of the semiconducting material. The mold 100 may remainimmersed in the molten semiconducting material 104 for a time sufficientfor the frozen semiconducting material to remelt and the mold 100 toreach a temperature such that the temperature of the mold, T_(Mold), mayequilibrate with the temperature of the molten semiconducting material,T_(Melt) (i.e., T_(Mold)=T_(Melt)). The immersion of mold 100 mayoptionally be repeated additional times to thermally equilibrate mold100 with the molten semiconducting material 104.

The amount of time sufficient for the semiconducting material tofreeze/solidify and remelt is within the ability of those skilled in theart to determine based on variables such as, for example, thesemiconducting material, the material comprising the mold, the amount ofundercooling, and the thickness of the mold. For example, for a moldhaving a thickness of about 2 mm, the amount of time over which freezingtakes place may be up to about 5 seconds, such as, for example, about 3seconds. For example, for a mold having a thickness of about 2 mm, theamount of time over which remelting takes place may be up to about 60seconds, such as, for example, about 40 seconds.

A representative calculated plot of the thickness of a silicon articleformed as a function of the immersion time in molten silicon during thefreezing-remelting process is shown in FIG. 2. As seen in FIG. 2, thethickness of the solidified layer rapidly increases and then slowlydecreases to zero. The instantaneous velocity of the growth of thesolid-liquid interface perpendicular to the surface of mold 100 can becalculated using the Stefan condition (Equation 1)

$\begin{matrix}{\left. {K_{S}\frac{\partial T}{\partial x}} \middle| {}_{S}{{- K_{L}}\frac{\partial T}{\partial x}} \right|_{L} = {v_{i}\rho_{s}\lambda}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$

where K_(S) and K_(L) are the thermal conductivities of the solid andliquid phases, respectively, v_(i) is the instantaneous interfacevelocity, ρ_(s) is the density of the solid, T is the temperature, x isthe position normal to the solid-liquid interface, λ the latent heat offusion, and S and L denote solid and liquid phases, respectively. Thefirst and second terms on the left side of Equation 1 are the heatfluxes through the solid and the liquid phases, respectively. If theheat flux through the solid is larger than the heat flux thorough theliquid, then the interface velocity is positive and freezing continues.Conversely, if the heat flux through the liquid is higher than the heatflux thorough the solid, the interface velocity is negative andremelting takes place.

When the mold is initially immersed in the molten semiconductormaterial, i.e., during the freezing phase, the heat flux through thesolid phase may be much larger than that through the initiallyisothermal liquid, and therefore rapid solidification into the liquidtakes place. The solidification continues until the heat fluxes throughthe liquid and the solid become equal. Beyond this point, the heat fluxthrough the liquid is higher than that through the solid and remeltingstarts. During the remelting phase, latent heat is supplied to theinterface from the liquid melt. Therefore, during this phase, the liquidside thermal properties control the remelting dynamics. The remeltingprocess may continue until the initially frozen solid is completelymelted and the mold thermally equilibrates with the moltensemiconducting material.

The amount of time it takes for the frozen semiconducting material toremelt may be approximately determined by Equations 2 and 3

$\begin{matrix}{t_{remelt} = {{{- \frac{d_{Mold}^{2}}{8\; \alpha_{Mold}}}{\ln \left( {1 - f} \right)}} + {\Delta^{2}\pi \; {\alpha_{Melt}\left( \frac{\rho_{Melt}\lambda}{2{K_{Melt}\left( {T_{M} - T_{Melt}} \right)}} \right)}^{2}}}} & {{Eq}.\mspace{14mu} 2} \\{\Delta = {\frac{1}{2}\left\lbrack \frac{\rho_{Mold}{Cp}_{Mold}{d_{Mold}\left( {T_{M} - T_{0}} \right)}}{{\rho_{Melt}\lambda} + {\rho_{Melt}{{Cp}_{Melt}\left( {T_{Melt} - T_{M}} \right)}}} \right\rbrack}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

where t_(remelt) is the complete remelting time, d_(Mold) is the moldthickness, α_(Mold) is the thermal diffusivity of the mold, ρ_(Mold) isthe density of the mold, Cp_(Mold) is the heat capacity of the mold, andΔ is the maximum thickness of semiconducting material formed on thesurface of the mold. The quantities α_(Melt) and Cp_(Melt) are thethermal diffusivity and heat capacity of the molten semiconductingmaterial, respectively. The density and thermal conductivity of themolten semiconducting material are ρ_(Melt) and K_(Melt), respectively,and λ is the latent heat. T_(M) is the melting temperature of thesemiconducting material, T₀ is the initial temperature of the mold, andT_(Melt) is the bulk temperature of the molten semiconducting material.The expression for the mold temperature increase is exponential. Thus, aquantity, f, wherein 0<f<1, is introduced to yield an approximate timeat which the temperature of the mold, T_(Mold), is sufficiently equal tothe temperature of the molten semiconducting material, T_(Melt). In atleast one embodiment, the remelting time, t_(remelt), may be calculatedusing a value of f equal to 0.9.

Once the frozen layer of semiconducting material has substantiallyremelted and the temperature of the mold, T_(Mold), reachesapproximately the temperature of the molten semiconducting material,T_(Melt), mold 100 may be removed from the molten semiconductingmaterial 104 and allowed to cool. The amount of time sufficient for themold to substantially thermally equilibrate with the moltensemiconducting material is within the ability of those skilled in theart to determine and may be based on variables such as, for example, thematerial comprising the mold, the semiconducting material, the thicknessof the mold, and the amount of undercooling. For example, a 2 mm thickfused silica mold may thermally equilibrate with the moltensemiconducting material in about 50 seconds.

The mold 100 may cool by radiation and/or convection after it is removedfrom the molten semiconducting material. At high temperatures, radiationmay dominate the cooling process and the temperature of mold 100 may beapproximated by Equation 4

$\begin{matrix}{\frac{1}{T_{Mold}^{3}} = {\frac{1}{T_{Melt}^{3}} + {\frac{6\; ɛ_{Mold}\sigma}{d_{Mold}\rho_{Mold}{Cp}_{Mold}}t}}} & {{Eq}.\mspace{14mu} 4}\end{matrix}$

where T_(Mold) is the temperature of the mold at time t, T_(Melt) is thetemperature of the mold at the time immediately prior to removal fromthe molten semiconducting material (i.e., the temperature of the melt),ε_(Mold) is the emissivity of the mold, σ is the Stefan-Boltzmannconstant, ρ_(Mold) is the density of the mold, Cp_(Mold) is the heatcapacity of the mold, d_(Mold) is the thickness of the mold, and t istime.

A plot of the temperature of an exemplary mold 100 as a function of timeafter removing the mold 100 from the molten semiconducting material 104is shown in FIG. 3. FIG. 3 compares the calculated temperature T_(Mold)(solid line) and actual experimental measurements (dotted line)according to an embodiment of the invention. A graph of the cooling timeafter the mold 100 is removed from the molten semiconducting material104 as a function of the amount of desired undercooling (i.e.,T_(melt)−T_(Mold)=amount of undercooling) is shown in FIG. 4. In FIG. 4,the solid line represents a mold having a thickness of 1 mm, the dottedline represents a mold having a thickness of 1.6 mm, and the line ofdashes and dots represents a mold having a thickness of 3 mm. As seen inFIG. 4, thicker molds may take a greater amount of time to reach thesame amount of undercooling as thinner molds.

In at least one embodiment, mold 100 may be immersed in the moltensemiconducting material 104 a second time after a set or predeterminedamount of undercooling has been reached. For example, a 2 mm fusedsilica mold undercooled by 400 K may be immersed for about 1 sec toabout 4 sec, such as from about 1 sec to about 3 sec. Without wishing tobe bound by theory, it is believed that reducing the amount ofundercooling decreases the nucleation rate on the mold. A graph of thenucleation rate as a function of the amount of undercooling is shown inFIG. 7 for molds made of silicon carbide (M₁) and fused silica (M₂), aswell as for homogeneous nucleation (H). It is believed that reducing thenucleation rate may improve the crystal grain structure of solidifiedsemiconducting material.

Initial crystal growth may extend substantially planar to the surface ofthe mold 100 until the surface of the mold 100 is substantially coveredand the individual grains impinge on one another. Limiting thenucleation rate may reduce the number of grains formed and may thusimprove the crystal grain structure of the semiconducting material. Oncethe surface of the mold 100 has been substantially covered withsolidified semiconducting material, growth occurs mainly normal to thesurface of the mold 100, and/or parallel to the direction of heat flow.Reducing the amount of undercooling, however, may limit the maximumpossible thickness of the semiconducting material. The maximumthickness, Δ, of the semiconducting material formed on the surface ofmold 100 may be estimated using Equation 3, above.

A graph comparing the thicknesses of articles of semiconductingmaterials made according to an embodiment of the invention by a moldundercooled by 1000° C., represented by the dashed line, and a moldundercooled by 400° C., represented by the solid line, as a function oftime is shown in FIG. 5. In at least one embodiment, the predeterminedamount of undercooling may be chosen based on the desired thicknessand/or grain structure of the produced article of semiconductingmaterial.

According to at least one embodiment, as shown in FIGS. 1 and 8, mold100 may be immersed in the molten semiconducting material 104 at a setor predetermined rate, optionally in a low oxygen or reducingatmosphere. Mold 100 may be immersed in molten semiconducting material104 at any immersion angle θ, where immersion angle θ is the anglebetween the surface 108 of molten semiconducting material 104 and theexternal surface 102 of mold 100 at the point P that first contacts thesurface 108 of molten semiconducting material 104 as shown in FIG. 8.The angle at which external surface 102 of mold 100 contacts moltensemiconducting material 104 may vary as mold 100 is immersed in moltensemiconducting material 104. Byway of example only, in one embodiment,molten semiconducting material could contact a mold having a sphericalexternal surface at an infinite number of angles as it is immersed,although the immersion angle θ would be 0° as the initial contact pointwould be parallel to the surface 108 of molten semiconducting material104. In further exemplary embodiments, mold 100 may be moved in adirection parallel to surface 108 of molten semiconducting material 104as mold 100 is immersed in a direction perpendicular to surface 108 ofmolten semiconducting material 104. Such parallel motion may includetranslation of the mold at a set or variable rate, or vibration of themold at a set or variable frequency. One skilled in the art would alsorecognize that the local immersion angle, which is the immersion angleat any finite location at the point P of first contact, may also varydue to the surface properties (such as, for example, porosity or heightvariations) and the wetting angle between the melt and the materialcomprising the mold.

In a further exemplary embodiment, external surface 102 of mold 100 maybe substantially perpendicular to the surface 108 of the moltensemiconducting material 104, i.e., the immersion angle is approximately90°. In a further embodiment, the external surface 102 of mold 100 neednot be perpendicular to the surface 108 of molten semiconductingmaterial 104. By way of example, the external surface 102 of mold 100may be immersed in the molten semiconducting material 104 at animmersion angle ranging from 0° to 180°, such as from 0° to 90°, from 0°to 30°, from 60° to 90°, or at an immersion angle of 45°.

In at least one embodiment of the invention, mold 100 may be immersed inthe molten semiconducting material 104 at least two times. According toat least one embodiment, mold 100 is immersed in the moltensemiconducting material 104 more than two times. In at least oneembodiment of the invention, immersion of the mold may be accomplishedusing any suitable technique, and may be accomplished by immersing themold from above the molten semiconducting material or from the side orbottom of the molten semiconducting material.

In at least one embodiment, mold 100 may be immersed in the moltensemiconducting material 104 for a set or predetermined time (i.e., theimmersion time) to allow a layer of the semiconducting material tosufficiently solidify over a surface 102 of mold 100. In at least oneembodiment, the semiconducting material is sufficiently solidified whenenough semiconducting material has solidified that the mold can bewithdrawn from the molten semiconducting material and the layer ofsemiconducting material will be withdrawn with the mold. According to atleast one embodiment, the immersion time is chosen based on the desiredthickness of the produced article of semiconducting material. In atleast one embodiment, at least one heating element 109, such asresistive heating elements or inductive heating elements, may be used toheat the crucible 106 and maintain the molten semiconducting material104 at a set or predetermined temperature while mold 100 is immersed. Inat least one embodiment, the bulk temperature of the moltensemiconducting material 104 may be maintained at approximatelytemperature, T_(Melt). The semiconducting material 104 may be melted andmaintained in molten form by any desired method, and the selection ofthe heating method would be within the skill of one in the art and maybe based on the conditions and environment where the method isperformed. In at least one embodiment, the method may be performed in areducing environment and may use radio frequency (RF) induction heatingto maintain the temperature of the molten semiconducting material. RFinduction heating may provide a cleaner environment by reducing thepossibility of the presence of foreign matter in the melt. Inductionheating may also provide the heat flux needed to maintain the desiredbulk molten material temperature as the material near the surface ofmold 100 extracts heat rapidly.

According to at least one embodiment, mold 100 may be held essentiallymotionless in the plane parallel to the surface 108 of moltensemiconducting material 104 as it is immersed in a directionperpendicular to surface 108 of molten semiconducting material 104. Inother embodiments, mold 100 may be moved in the plane parallel to thesurface 108 of molten semiconducting material 104, for example rotatedor vibrated at any appropriate frequency, when it is immersed in adirection perpendicular to the surface 108 of molten semiconductingmaterial 104. A layer of semiconducting material 110 may form on thesurface 102 of mold 100. After immersion, mold 100 with a layer ofsemiconducting material 110 may be withdrawn from the vessel 106. In atleast one embodiment, mold 100 with a solid layer of semiconductingmaterial 110 may be cooled after it is removed from vessel 106, eitheractively such as by convective cooling, or by allowing the temperatureof the layer of semiconducting material 110 to come to room temperature.After the coated mold 100 is removed from vessel 106 and sufficientlycooled, the solid layer of semiconducting material 110 may be removed orseparated from mold 100 by any method known to those of skill in theart. In at least one embodiment, the solid layer of semiconductingmaterial 110 may be separated from mold 100 by differential expansionand/or mechanical assistance.

In at least one embodiment, the semiconducting material is chosen fromsilicon, germanium, gallium arsenide, tin, as well as compounds, alloysand mixtures thereof. According to various embodiments of the invention,the semiconducting material may be pure or doped. In at least oneembodiment, the semiconducting material comprises at least one dopantchosen from boron (B), phosphorous (P), or aluminum (Al). In at leastone embodiment, the at least one dopant is present in the part permillion (ppm) range. The amount of dopant present in the moltensemiconducting material may be based on the desired dopant concentrationin the formed article of semiconducting material and may depend on thefinal use of the article, such as, for example, in a photovoltaic cell.According to at least one embodiment, an article of semiconductingmaterial produced by the methods disclosed herein may comprise a dopantdispersed substantially homogeneously throughout the semiconductingmaterial (e.g., without substantial segregation of the dopant within thesemiconducting material).

In at least one embodiment, the semiconducting material may comprisesemiconducting elements, such as, for example, silicon and germanium. Inat least one other embodiment, the semiconducting material comprises acombination or alloy of elements of compounds. For example, thesemiconducting material may be chosen from gallium arsenide (GaAs),aluminum nitiride (AlN), and indium phosphide (InP).

In at least one embodiment, a number of process parameters may bevaried, including but not limited to: (1) the composition, density, heatcapacity, thermal conductivity, thermal diffusivity, and thickness ofthe mold 100, (2) the starting temperature of mold, T₀, and the bulktemperature of the molten semiconducting material, T_(Melt), (3) therate which mold 100 is initially immersed into the molten material 104,(4) the length of time at which mold 100 is immersed a first time in themolten material 104, (5) the rate at which mold 100 is removed from themolten semiconducting material 104, (6) the time mold 100 is allowed tocool after the first immersion, (7) the rate at which mold 100 isimmersed into the molten material 104 after reaching the predeterminedamount of undercooling, (8) the rate at which mold 100 having the layerof semiconducting material 110 is removed from the molten material 104,and (9) the cooling rate of the solidified semiconducting material 110.In at least one embodiment, the temperature of molten semiconductingmaterial, T_(Melt), and the amount of time for undercooling mold 100 arethe only parameters that govern the temperature of mold 100 (i.e., thetemperature of the mold is not directly controlled by a heating orcooling device). The temperature of the molten semiconducting material,T_(Melt), may alter the temperature of mold 100 through radiation,convection, or conduction. Radiative heating of mold 100 may occur, forexample, when mold 100 is above molten semiconducting material 104. Mold100 may be convectively heated by molten semiconducting material 104when fumes above molten semiconducting material 104 pass over thesurface of mold 100 or during immersion of mold 100 in the moltensemiconducting material 104. Heating of mold 100 by conduction mayoccur, for example, while mold 100 is immersed in molten semiconductingmaterial 104.

In at least one embodiment, mold 100 is made of a material that iscompatible with the molten semiconducting material 104. For example,mold 100 may be made of a material such that when mold 100 is exposed tothe molten material 104, the principle material of mold 100 does notreact with the molten material 104 in a manner that interferes with themethods disclosed herein, such as, for example, by forming a low-meltingcompound or solid solution. As a further example, mold 100 may not meltor soften when mold 100 is heated via contact with the molten material104. In at least one embodiment, mold 100 may not become too fluid tosupport the solid layer 110 or separate from the solid layer 110 whenmold 100 is heated via contact with the molten material 104. In at leastone embodiment, mold 100 may be made of a material such that when mold100 is heated via contact with the molten material 104, mold 100 may notcheck, fracture, and/or explode due to either large thermal stressesgenerated from uneven, rapid thermal expansion, or from trapped gases.In at least one embodiment, mold 100 may be made of a material that maynot deleteriously contaminate either the solidified layer 110 beingformed on the mold or the molten material 104 residuum via breakage,spallation, dusting, and/or diffusion of vapor or liquid phases of solidcomponents or evolved gases. According to at least one embodiment, mold100 may comprise a material chosen from vitreous silica, fused silica,porous silica, graphite, silicon nitride, silicon carbide, andcombinations thereof. In at least one embodiment of the invention, mold100 may comprise vitreous silica.

In at least one embodiment of the invention, the mold may be a templatedmold. FIG. 6 shows a schematic illustration of a templated mold 200according to an embodiment of the invention. Templated mold 200 may havea primary substrate 201 and discrete locations 203 of at least onesecondary material that has lower contact angle with moltensemiconductor material than the contact angle between moltensemiconductor and the principle substrate 201. Discrete locations 203may have a low contact angle with the semiconducting material and may bemore likely to be the site of nucleation than the principle substrate201, which may have a high contact angle with the molten semiconductingmaterial.

In at least one embodiment of the invention, principle substrate 201 maycomprise fused silica, which has a contact angle of about 92°. Othermaterials that may comprise principle substrate 201 include poroussilica, silicon nitride, silicon carbide, graphite, alumina, aluminumnitride, boron nitride, LaB₆, zirconia, and yttria.

In at least one embodiment of the invention, discrete locations 203 of alow contact angle material may comprise silicon carbide, which has acontact angle of about 38°. Other materials that may comprise thediscrete locations 203 of low contact angle may be chosen from poroussilica, silicon nitride, alumina, aluminum nitride, boron nitride, LaB₆,zirconia, and yttria. The discrete locations 203 of low contact anglematerial may have any shape, including, for example, circles, squares,dots, islands, triangles, lines, random shapes, etc. In the exemplarytemplated mold shown in FIG. 6, discrete locations 203 of lower contactangle material are circular (diameter, d) and spaced at a distances a, bfrom neighboring discrete locations 203. In at least one embodiment, thecontact angle of the lower contact angle material may be at least 10°less than the contact angle of the higher contact angle material. Forexample, the lower contact angle material may have a contact angle atleast 40° less than the contact angle of the higher contact anglematerial.

In at least one embodiment of the invention, principle substrate 201 maycomprise fused silica and discrete locations 203 of lower contact anglematerial may comprise silicon carbide. As can be seen from the data inFIG. 7, nucleation occurs on silicon carbide at a lower amount ofundercooling than on fused silica. In other words, at the sameundercooling values, the nucleation rate on silicon carbide is muchhigher than that on fused silica. In at least one embodiment, the amountof undercooling may be chosen such that nucleation occurs substantiallyon the discrete locations 203 rather than on principle substrate 201.According to at least one embodiment, the amount of undercooling mayrange from 1 K to 500 K, such as from 10 K to 300 K, or from 50 K to 200K. According to at least one embodiment, the amount of undercooling maybe chosen such the nucleation rate on the lower contact angle materialis at least two times the nucleation rate of the higher contact anglematerial. For example, the nucleation rate on the lower contact anglematerial may be ten times or one hundred times greater than thenucleation rate of the higher contact angle material. One skilled in theart would recognize that the amount of undercooling may be chosen basedon the materials comprising the high contact angle material and the lowcontact angle material and the nucleation rates associated with eachmaterial.

Mold 100 may be in any form suitable for use in the disclosed methods.For example, in at least one embodiment, mold 100 may be in the form ofa monolith or in the form of a laminated structure such as a laminatedmonolith. Mold 100 may comprise a porous or non-porous body, optionallywith at least one porous or non-porous coating. In at least oneembodiment, mold 100 may also comprise a uniform or non-uniformcomposition, uniform or non-uniform porosity, or other uniform ornon-uniform structural characteristic throughout the mold body.According to at least one embodiment, mold 100 may also be in any shapesuitable for use in the disclosed method. For example, mold 100 maycomprise at least one flat surface (e.g., having a rectangular shape) orone or more curved surfaces, for example one or more convex or concavesurfaces. For example, the convex or concave surfaces may be used tocreate an article in the shape of a lens or a tube.

According to at least one embodiment, the rate at which the mold isimmersed into the molten material may range from 1 cm/s to 50 cm/s, suchas, for example, from 3 cm/s to 10 cm/s. One skilled in the art wouldrecognize that the immersion rate may vary depending on variousparameters, such as, for example, the semiconducting materialcomposition (including optional dopants), the size/shape of the mold,and the surface texture of the mold.

The withdrawal rate of the mold from the molten material may affect thesmoothness of the surface, thickness or other features of the solidarticle formed. When the mold is withdrawn from the moltensemiconducting material, a layer of molten semiconducting material maywet the surface of the solid layer of semiconducting material on themold, which may add thickness to the solid layer of semiconductingmaterial and/or may change the surface structure of the solid layer ofsemiconducting material. In at least one embodiment, solid articleshaving smooth surfaces may be made using a relatively slow withdrawalrate of the mold from the molten material, such as, for example, from 2cm/s to 5 cm/s, such as, for example, 5 cm/s. When the mold is pulledout quickly, small local variations in heat removal may manifest asisolated solidification events that trap extra liquid within them,forming puddles and bumps. As these puddles and bumps rapidly solidify,they may form blobs and faceted peaks, sometimes several millimeterstall and one or more centimeters wide. It is believed that slowerwithdrawal rates may confine the wetted area to the liquid-solid-gasinterface and may put a continuous secondary smooth layer on the surfaceof the solid layer. Furthermore, quickly moving the mold may induce flowpatterns and even turbulence in the melt. The coupling between flowmotion and heat transfer may cause pattern formation on the solidifiedsurface of the article. In at least one embodiment, an article ofsemiconducting material may be made by withdrawing the mold at a ratesuch that a secondary smooth layer is formed on the surface of the solidsemiconducting material layer.

The thickness of the secondary layer (i.e., drag layer) can be affectedby both how much liquid is dragged and how much of the dragged liquid issolidified. Generally, secondary liquid layer thickness increases withpulling velocity while the solidified layer thickness decreases withpulling velocity. By way of example, if heat transfer is limiting thethickness of the solidified layer, increasing the pulling velocity willdecrease the solidified layer thickness due to liquid dragging. Incontrast, if the dragged liquid is limited, increasing the pullingvelocity will increase the solidified layer thickness due to liquiddragging.

A person skilled in the art would recognize that the immersion rate,immersion time, and withdrawal rate all affect the produced article andthat these parameters may be chosen based on the desired article, thematerial/shape/texture/size of the mold, the starting temperature of themold, the temperature of the molten semiconducting material, and theproperties of the semiconducting material.

Returning again to FIG. 1, in at least one embodiment of the invention,vessel 106, which holds the molten semiconducting material 104, may notreact with the molten material 104 and/or may not contaminate the moltenmaterial 104, as described above for mold 100. In at least oneembodiment, vessel 106 may be made from a material chosen from vitreoussilica, graphite, silicon nitride, and silicon carbide. In at least oneembodiment, vessel 106 is made of vitreous silica.

Without wishing to be limited by theory, it is believed that in at leastcertain embodiments, the use of vitreous silica for the mold 104 and/orvessel 106 may lead to oxygen contamination of the semiconductingmaterial. Thus, in various embodiments, oxygen contamination may bemitigated or substantially mitigated by melting the semiconductingmaterial and casting the article in a low-oxygen environment, such as,for example, a dry mixture of hydrogen (<1 ppm of water) and an inertgas such as argon, krypton or xenon. In at least one exemplaryembodiment, the atmosphere is chosen from an Ar/1.0 wt % H₂ mixture orAr/2.5 wt % H₂ mixture.

In at least one embodiment, mold 100 may have an external surface 102which is flat. In at least one embodiment, mold 100 may have an externalsurface 102 with characteristics to form articles with a broad range ofshapes, curvatures, and/or textures. As would be understood by oneskilled in the art, any other surface texture/pattern desired in thecast article may be incorporated in the external surface 102 of mold100.

In at least one embodiment, the disclosed method may be used to make asheet or film of semiconducting material, such as, for example, asilicon sheet, having a size, thickness, and grain structure within therange of usefulness for photovoltaic applications, for example, size upto approximately 156 mm×156 mm, thickness in a range of 100-400micrometers, and a substantial number of grains larger than 1 mm.According to at least one embodiment, at least about 60% of the grainsmay be larger than 1 mm. In a further embodiment, at least about 80% orat least about 90% of the grains may be larger than 1 mm. In at leastone embodiment, the grains are two to three times greater in size intheir narrowest lateral direction than they are thick.

In at least one embodiment, the disclosed method yields an article ofsemiconducting material at an improved rate and/or a reduction in wastedmaterial. For example, the exocasting processes described herein can beperformed with essentially no waste of semiconducting material, sinceall the melted material can be cast into a useful article. Any brokenpieces or other unused material can be remelted and cast again. In atleast one embodiment, immersion cycle times of less than 5 seconds areused to form sheets 7 cm in length (independent of width), whichtranslates to a process speed of a few centimeters per second.

Unless otherwise indicated, all numbers used in the specification andclaims are to be understood as being modified in all instances by theterm “about,” whether or not so stated. It should also be understoodthat the precise numerical values used in the specification and claimsform additional embodiments of the invention. Efforts have been made toensure the accuracy of the numerical values disclosed herein. Anymeasured numerical value, however, can inherently contain certain errorsresulting from the standard deviation found in its respective measuringtechnique.

It is noted that, as used in this specification and the appended claims,the singular forms “a,” “an,” and “the,” include plural referents unlessexpressly and unequivocally limited to one referent, and vice versa.Thus, by way of example only, reference to “a heat source” can refer toone or more heat sources, and reference to “a semiconducting material”can refer to one or more semiconducting materials. As used herein, theterm “include” and its grammatical variants are intended to benon-limiting, such that recitation of items in a list is not to theexclusion of other like items that can be substituted or added to thelisted items.

It will be apparent to those skilled in the art that variousmodifications and variation can be made to the programs and methods ofthe present disclosure without departing from the scope its teachings.Other embodiments of the disclosure will be apparent to those skilled inthe art from consideration of the specification and practice of theteachings disclosed herein. It is intended that the embodimentsdescribed in the specification be considered as exemplary only.

1. A method of making an unsupported article of a semiconductingmaterial, comprising: providing a mold at a temperature T₀; providing amolten semiconducting material at a bulk temperature T_(Melt), whereinT_(Melt)≧T₀; immersing the mold in the molten semiconducting material atleast once for a first period of time sufficient to form a solid layerof the semiconducting material over an external surface of the mold andfor the formed solid layer of semiconducting material to completelyremelt; withdrawing the mold from the molten semiconducting material;holding the mold above the molten semiconducting material for a periodof time sufficient to undercool the mold a predetermined amount;immersing the mold in the molten semiconducting material for a secondperiod of time sufficient to form a solid layer of the semiconductingmaterial over the external surface of the mold; withdrawing the moldwith the solid layer of semiconducting material on the external surfaceof the mold; and separating the solid layer of semiconducting materialfrom the mold to form the unsupported article of the semiconductingmaterial.
 2. The method of claim 1, wherein the semiconducting materialis chosen from silicon, alloys and compounds of silicon, germanium,alloys and compounds of germanium, gallium arsenide, alloys andcompounds of gallium arsenide, tin, alloys and compounds of tin, andmixtures thereof.
 3. The method of claim 1, wherein the semiconductingmaterial is chosen from silicon, silicon alloys, and silicon compounds.4. The method of claim 3, wherein T_(Melt) ranges from about 1414° C. toabout 1550° C.
 5. The method of claim 1, wherein the first period oftime of mold immersion is equal to t_(remelt), wherein:$t_{remelt} = {{{- \frac{d_{Mold}^{2}}{8\; \alpha_{Mold}}}{\ln \left( {1 - f} \right)}} + {\Delta^{2}\pi \; {\alpha_{Melt}\left( \frac{\rho_{Melt}\lambda}{2{K_{Melt}\left( {T_{M} - T_{Melt}} \right)}} \right)}^{2}}}$${{{and}\mspace{14mu} \Delta} = {\frac{1}{2}\left\lbrack \frac{\rho_{Mold}{Cp}_{Mold}{d_{Mold}\left( {T_{M} - T_{0}} \right)}}{{\rho_{Melt}\lambda} + {\rho_{Melt}{{Cp}_{Melt}\left( {T_{Melt} - T_{M}} \right)}}} \right\rbrack}},$wherein d_(Mold) is a thickness of the mold, α_(Mold) is a thermaldiffusivity of the mold, ρ_(Mold) is a density of the mold, Cp_(Mold) isa heat capacity of the mold, Δ is a maximum thickness of semiconductingmaterial formed on the external surface of the mold, α_(Melt) is athermal diffusivity of the molten semiconducting material, Cp_(Melt) isa heat capacity of the molten semiconducting material, ρ_(Melt) is adensity of the molten semiconducting material, K_(Melt) is thermalconductivity of the molten semiconductor material, λ is latent heat,T_(M) is a melting temperature of the semiconducting material, T₀ is thetemperature at which the mold is provided, T_(Melt) is the bulktemperature of the molten semiconducting material, and 0<f<1.
 6. Themethod of claim 1, wherein the mold is undercooled by an amount rangingfrom about 1 K to about 500 K.
 7. The method of claim 1, wherein themold is undercooled for a period of time, t, wherein:$t = {\left( \frac{d_{Mold}\rho_{Mold}{Cp}_{Mold}}{6\; ɛ_{Mold}\sigma} \right)\left( {\frac{1}{T_{Mold}^{3}} - \frac{1}{T_{Melt}^{3}}} \right)}$wherein T_(Mold) is the temperature of the mold for the predeterminedamount of undercooling, T_(Melt) is the bulk temperature of the melt,ε_(Mold) is an emissivity of the mold, σ is the Stefan-Boltzmannconstant, ρ_(Mold) is a density of the mold, Cp_(Mold) is a heatcapacity of the mold, d_(Mold) is a thickness of the mold, and t is thetime to hold the mold above the molten semiconducting material.
 8. Themethod of claim 1, wherein the mold is made of a material chosen fromvitreous silica, porous silica, fused silica, silicon nitride, siliconcarbide, graphite, alumina, aluminum nitride, boron nitride, LaB₆,zirconia, and yttria.
 9. The method of claim 1, wherein the mold is atemplated mold comprising at least two materials having differentcontact angles with the molten semiconducting material.
 10. The methodof claim 9, wherein the templated mold comprises fused silica andsilicon carbide.
 11. The method of claim 9, wherein the at least twomaterials have contact angles that differ by at least 10°.
 12. Themethod of claim 1, wherein an atmosphere above the molten semiconductingmaterial comprises argon and hydrogen.
 13. A method of making anunsupported article of a semiconducting material, comprising: providinga mold at a temperature T₀, wherein the mold comprises a principlesubstrate and discrete locations comprising a material having a contactangle with the molten semiconducting material lower than a contact anglebetween the molten semiconducting material and the principle substrate;providing a molten semiconducting material at a bulk temperatureT_(Melt), wherein T_(Melt)≧T₀; immersing the mold in the moltensemiconducting material at least once for a first period of timesufficient to form a solid layer of the semiconducting material over anexternal surface of the mold and for the formed solid layer ofsemiconducting material to completely remelt; withdrawing the mold fromthe molten semiconducting material; holding the mold above the moltensemiconducting material for a period of time sufficient to undercool themold a predetermined amount; immersing the mold in the moltensemiconducting material for a second period of time sufficient to form asolid layer of the semiconducting material over the external surface ofthe mold; withdrawing the mold with the solid layer of semiconductingmaterial on the external surface of the mold; and separating the solidlayer of semiconducting material from the mold to form the unsupportedarticle of the semiconducting material.
 14. The method of claim 13,wherein the principle substrate is chosen from vitreous silica, fusedsilica, porous silica, silicon nitride, silicon carbide, graphite,alumina, aluminum nitride, boron nitride, LaB₆, zirconia, and yttria.15. The method of claim 13, wherein the discrete locations of lowercontact angle are chosen from fused silica, porous silica, siliconnitride, silicon carbide, alumina, aluminum nitride, boron nitride,LaB₆, zirconia, and yttria.
 16. The method of claim 13, wherein theprinciple substrate has a contact angle at least 10° greater than thecontact angle of the discrete locations of lower contact angle material.17. The method of claim 13, wherein the mold is undercooled by an amountranging from about 1 K to about 500 K.
 18. The method of claim 13,wherein the mold is undercooled for a period of time, t, wherein:$t = {\left( \frac{d_{Mold}\rho_{Mold}{Cp}_{Mold}}{6\; ɛ_{Mold}\sigma} \right)\left( {\frac{1}{T_{Mold}^{3}} - \frac{1}{T_{Melt}^{3}}} \right)}$wherein T_(Mold) is the temperature of the mold for the predeterminedamount of undercooling, T_(Melt) is the bulk temperature of the melt,ε_(Mold) is an emissivity of the mold, σ is the Stefan-Boltzmannconstant, ρ_(Mold) is a density of the mold, Cp_(Mold) is a heatcapacity of the mold, d_(Mold) is a thickness of the mold, and t is thetime to hold the mold above the molten semiconducting material.
 19. Themethod of claim 13, wherein the first period of time of mold immersionis equal to t_(remelt), wherein:$t_{remelt} = {{{- \frac{d_{Mold}^{2}}{8\; \alpha_{Mold}}}{\ln \left( {1 - f} \right)}} + {\Delta^{2}\pi \; {\alpha_{Melt}\left( \frac{\rho_{Melt}\lambda}{2{K_{Melt}\left( {T_{M} - T_{Melt}} \right)}} \right)}^{2}}}$${{{and}\mspace{14mu} \Delta} = {\frac{1}{2}\left\lbrack \frac{\rho_{Mold}{Cp}_{Mold}{d_{Mold}\left( {T_{M} - T_{0}} \right)}}{{\rho_{Melt}\lambda} + {\rho_{Melt}{{Cp}_{Melt}\left( {T_{Melt} - T_{M}} \right)}}} \right\rbrack}},$wherein d_(Mold) is a thickness of the mold, α_(Mold) is a thermaldiffusivity of the mold, ρ_(Mold) is a density of the mold, Cp_(Mold) isa heat capacity of the mold, Δ is a maximum thickness of semiconductingmaterial formed on the external surface of the mold, α_(Melt) is athermal diffusivity of the molten semiconducting material, Cp_(Melt) isa heat capacity of the molten semiconducting material, ρ_(Melt) is adensity of the molten semiconducting material, K_(Melt) is thermalconductivity of the molten semiconductor material, λ is latent heat,T_(M) is a melting temperature of the semiconducting material, T₀ is thetemperature at which the mold is provided, T_(Melt) is the bulktemperature of the molten semiconducting material, and 0<f<1.
 20. Themethod of claim 13, wherein an atmosphere above the moltensemiconducting material comprises argon and hydrogen.
 21. The method ofclaim 13, wherein the semiconducting material is chosen from silicon,alloys and compounds of silicon, germanium, alloys and compounds ofgermanium, gallium arsenide, alloys and compounds of gallium arsenide,tin, alloys and compounds of tin, and mixtures thereof.
 22. The methodof claim 21, wherein the semiconducting material is chosen from silicon,silicon alloys, and silicon compounds.
 23. The method of claim 22,wherein T_(Melt) ranges from about 1414° to about 1550° C.
 24. Anunsupported article of semiconducting material formed by a methodcomprising: providing a mold at a temperature T₀; providing a moltensemiconducting material at a bulk temperature T_(Melt), whereinT_(Melt)≧T₀; immersing the mold in the molten semiconducting material atleast once for a first period of time sufficient to form a solid layerof the semiconducting material over an external surface of the mold andfor the formed solid layer of semiconducting material to completelyremelt; withdrawing the mold from the molten semiconducting material;holding the mold above the molten semiconducting material for a periodof time sufficient to undercool the mold a predetermined amount;immersing the mold in the molten semiconducting material for a secondperiod of time sufficient to form a solid layer of the semiconductingmaterial over the external surface of the mold; withdrawing the moldwith the solid layer of semiconducting material on the external surfaceof the mold; and separating the solid layer of semiconducting materialfrom the mold to form the unsupported article of the semiconductingmaterial.
 25. The unsupported article of semiconducting material ofclaim 24, wherein the semiconducting material is chosen from silicon,alloys and compounds of silicon, germanium, alloys and compounds ofgermanium, gallium arsenide, alloys and compounds of gallium arsenide,tin, alloys and compounds of tin, and mixtures thereof.
 26. Theunsupported article of semiconducting material of claim 24, wherein thesemiconducting material is chosen from silicon, alloys of silicon, andcompounds of silicon.
 27. The unsupported article of semiconductingmaterial of claim 24, wherein grains of the semiconducting material havea narrowest lateral dimension two to three times a thickness of thegrains.